I am attempting to evaporate water to the atmosphere with a boiler type vessel. Normal operating pressure of the vessel would be 5 psig. How much water could potentially be evaporated? Also, what issues come to mind with this concept?

If you are evaporating to Atmosphere, there is no limit to the amount of water that could be evaporated.
However if you are limited to 5 psi over atmospheric, there will be a limit to how fast you can evaporate the water.

The actual limit will depend on lots of details you have not supplied;

The energy rate available from your source of heat
The amount of Water,
The size of your Boiler,
The size of the Vent from your Boiler to Atmosphere,
etc...

You can estimate the rate of evaporation using the equation for latent heat transfer:

$\displaystyle \dot{m} = \frac{\dot{Q}}{h_{liq-vap}}$

where m is the evaporation rate (in kg/s), Q is the rated power output of your boiler (in W) and $\displaystyle h_{liq-vap}$ is the specific enthalpy of liquid-to-vapour phase change of water.

At room temperature and pressure, $\displaystyle h_{liq-vap} = 2265 $ kJ/kg, but it's actually a function of temperature and pressure, so it's probably a little bit lower than this. You should recalculate this constant at the boiling point of water at that pressure (which I think is about 108 deg. C at 134 kPa).